We consider a robot with a mobile base joined to a body, also called upper body.
The normal forces acting by the wheels of the mobile base on the ground are strongly dependant of the position and acceleration of its body. So the mobile base suffers of strong slippages. Also, due to the important height of the robot in comparison with its support base dimension, the robot can easily fall.
In the literature, some papers can be found about the control of a mobile robot with dynamic stability constraints, and about the control of humanoid two-legged robots.
Some recent works deal with controlling a robot with dynamical constraints, caused by limbs such as manipulator arm. K. Mingeuk and al. have worked on the stabilization of a wheeled platform using dynamic constraints: “Stabilization of a rapid four-wheeled mobile platform using the zmp stabilization method”. They use a direct linear quadratic regulator (LQR) method to control the platform. The inconvenient of this method is that the submitted dynamic constraints require having the CoP (Center of Pressure) on the middle of the platform. The CoP is the barycenter of the contact forces between the robot and the ground. This method involves losing several DoF (Degree of Freedom): indeed, to prevent a robot from falling, the CoP needs to be only in the convex polygon defined by the contact points between the wheels and the ground.
In another paper, Y. Li and al. present a simple controller of a mobile robot with dynamic constraints: “The dynamic stability criterion on the wheel-based humanoid robot based on zmp modeling”. The difference with the K. Mingeuk and Al. publication is that it takes into account the full CoP constraint, which is a sum of inequality constraints. This controller is a pid-control iterated on a complete model of the robot to find a torque command where the CoP is in the support polygon.
Concerning humanoid robotics, P. B. Wieber, H. Diedam and A. Herdt have described a method to control humanoid two-legged robot with highly constrained dynamic: “Walking without thinking about it”. This most recent approach concerns the linear predictive control based on a 3d linear inverted pendulum model. Using a simple model of the robot, this control law predicts the dynamic of its state in the future, in order to ensure that the current command sent to the robot will not cause an inevitable fall in a few seconds. Concerning the biped humanoid robot NAO, an implementation of this control law can be found in a paper written by D. Gouaillier, C. Collette and K. Kilner: “Omni-directional closed-loop walk for nao”. But the robot NAO is small and this method would not give good results notably for a higher humanoid robot as shown FIG. 1, for instance with the following features:
20 Degrees of freedom (DoF) (2 DoF on the head 160, 2×6 DoF on the arms 170, 3 DoF on the leg 180 and 3 DoF in the mobile base 140); indeed a humanoid robot has at least 5 DoF (1 DoF for the head, 1 for each leg, 1 for each arm),
1.37 m height 110,
0.65 m width 130,
0.40 m depth 120,
30 kg total mass,
one leg 180 linked to the omnidirectionnal base 140 with three wheels 141. The mobile base has a triangular shape of 0.422 m length and is able to move the robot at a maximum velocity of 1:4 m/s−1 and acceleration of 1:7 m/s−2 for a short time. The nominal velocity and acceleration are 0:5 m/s−1 and 1:0 m/s−2.
A solution is to design a robot with a large omnidirectionnal base compared to the height of the robot; but then we have the following drawbacks: an overdue required space and a weakness of the robot's body.
There is therefore a need for controlling both the mobile base of a humanoid robot and its body, while taking into account their dynamical constraints.